This book popped back into my mind the other day, and I can't for the life of me remember its title or author. The cover was an image of a baby dragon emerging from an egg as a boy watches, amazed.
I don't remember much of the plot, except that it involved a boy of primary-school age obtaining this strange (rainbow-coloured?) egg from somewhere, a baby dragon hatching from the egg, and then the troubles the boy had trying to keep a little dragon as a pet. The story took place in the real world, not a fantasy world, i.e. the existence of a dragon was very remarkable. :)
To clarify after a couple comments: the baby dragon was kitten- or cat-sized for the part of the book I remember; this wasn't a case of a "baby" dragon still being much larger than the boy, D&D-style.
I read this book sometime in the (probably mid-)1990s. I suspect it was published around then, and I may have got it from one of the Scholastic book sales they'd run at my school. Anyway, it was a children's/YA book, not an adult novel.